Fig 1.
The flowchart of PFAGM model.
Table 1.
Comparison of different grey models for non-homogeneous exponential sequences with various development coefficients (X(0)(k) = Aeλ(k−1) + B, k = 1, 2, ⋅, n).
Table 2.
Comparison of different grey models for non-homogeneous exponential sequences with various development coefficients (X(0)(k) = Aeλ(k−1) + B(k − 1), k = 1, 2, ⋅, n).
Table 3.
Raw data of special non-homogeneous exponential sequences.
Fig 2.
Different non-homogeneous exponential sequences.
Table 4.
Comparison of different grey models for special non-homogeneous exponential sequences.
Table 5.
Raw data in Example A.
Table 6.
The optimal parameters of different grey models in Example A.
Table 7.
The results produced by proposed model and other comparative grey models in Example A.
Fig 3.
Searching optimal fractional order of PFAGM by using WOA for Example A.
Fig 4.
Performance comparison of the proposed model and other comparative grey models in Example A.
Fig 5.
Analysis of detailed results obtained by using the proposed model and other comparative grey models in Example A.
Table 8.
Raw data of cumulative oil field production in example B.
Table 9.
The optimal parameters of different grey models in Example B.
Table 10.
The results produced by proposed model and other comparative grey models in Example B.
Fig 6.
Searching optimal fractional order of PFAGM by using WOA for Example B.
Fig 7.
Performance comparison of the proposed model and other comparative grey models in Example B.
Fig 8.
Analysis of detailed results obtained by using the proposed model and other comparative grey models in Example B.
Table 11.
Raw data of foundation settlement in Example C.
Table 12.
The optimal parameters of different grey models in Example C.
Table 13.
The results produced by proposed model and other comparative grey models in Example C.
Fig 9.
Searching optimal fractional order of PFAGM by using WOA for Example C.
Fig 10.
Performance comparison of the proposed model and other comparative grey models in Example C.
Fig 11.
Analysis of detailed results obtained by using the proposed model and other comparative grey models in Example C.
Fig 12.
Rankings of different grey models in validations.
Table 14.
Raw data of China’s wind energy consumption (million tonnes oil equivalent).
Fig 13.
Searching optimal order of PFAGM by using WOA for forecasting Chinese wind energy consumption.
Table 15.
The optimal parameters of different grey models for forecasting Chinese wind energy consumption.
Table 16.
The results produced by different grey models for Chinese wind energy consumption.
Table 17.
China’s wind energy consumptions from 2019 to 2021 predicted by different grey models.
Fig 14.
Performance comparison of the proposed and other comparative grey models for forecasting Chinese wind energy consumption.
Fig 15.
Analysis of detailed results obtained by using the proposed model and other comparative grey models for forecasting Chinese wind energy consumption.